Details

sample26.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	40	9
2	78	9
3	134	9
4	200	9
5	233	9
6	239	9
7	239	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize9.0ms

Local error

Found 2 expressions with local error:

3.4b	(- (* x x) (* (* y 4.0) y))
31.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

3.0ms	(- (* x x) (* (* y 4.0) y))
11.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (* x x) (* (* y 4.0) y))
71.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify47.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	237	617
1	1114	565
2	5002	555

prune151.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune7.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

2.2b	(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.4b	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
16.8b	(/ (fma x x (* (* y 4.0) y)) x)
19.2b	(/ (fma x x (* (* y 4.0) y)) y)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

124×	`times-frac`
76×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`associate-/r*`
25×	`add-exp-log` `add-cbrt-cube`
11×	`cbrt-undiv` `div-exp`
10×	`div-inv` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `associate-/r/` `cbrt-unprod`

Counts

4 → 178

Calls

4 calls:

9.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
6.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
2.0ms	(/ (fma x x (* (* y 4.0) y)) x)
2.0ms	(/ (fma x x (* (* y 4.0) y)) y)

series276.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
67.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
81.0ms	(/ (fma x x (* (* y 4.0) y)) x)
66.0ms	(/ (fma x x (* (* y 4.0) y)) y)

simplify114.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	613	1740
1	3220	1580
2	5001	1580

prune489.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
1.9b	(log1p (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
3.4b	(- (* x x) (* (* y 4.0) y))
31.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log1p-udef` `expm1-log1p` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `log1p-expm1` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv` `expm1-udef`

Counts

4 → 72

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
0.0ms	(log1p (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
3.0ms	(- (* x x) (* (* y 4.0) y))
11.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
150.0ms	(log1p (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
51.0ms	(- (* x x) (* (* y 4.0) y))
66.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	283	903
1	1211	811
2	5002	798

prune254.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

52% (15.4b remaining)

Error of 15.7b against oracle of 0.3b and baseline of 32.4b

bsearch359.0ms

Steps

Iters	Range		Point
8	3.047530528666286e+89	2.1241537053097443e+92	3.0944404152107775e+89
8	1.933364594733743e-77	8.217386779769018e-74	9.970510408474918e-75
9	9.460430943576418e-137	8.911523066933264e-132	1.98441937058913e-132
8	-1.1339744629944117e-161	-1.770813970512317e-165	-3.4929772319374073e-162
6	-5.2407857676746225e-101	-1.3034355320647412e-101	-4.388460522981548e-101
7	-5.906728328883236e-65	-2.3197842709371557e-67	-3.2469602603904245e-67
9	-7.976204077621993e-23	-7.867221224566218e-28	-7.890596918911126e-23
5	-9.126032191279896e+27	-3.314665875535389e+27	-3.9547679581202103e+27

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	34
1	48	34

end0.0ms

sample703.0ms

Algorithm

intervals

Results

563.0ms

8000×

body

valid